[Zurück]

M. Aurada, M. Ebner, M. Feischl, S. Ferraz-Leite, T. Führer, P. Goldenits, M. Karkulik, M. Mayr, D. Praetorius:
"HILBERT - A MATLAB implementation of adaptive 2D-BEM";
Numerical Algorithms, 67 (2014), 1; S. 1 - 32.

We report on the Matlab program package HILBERT. It provides an
easily-accessible implementation of lowest order adaptive Galerkin
boundary element methods for the numerical solution of the Poisson
equation in 2D. The library was designed to serve several purposes:
The stable implementation of the integral operators may be used in
research code. The framework of Matlab ensures usability in lectures
on boundary element methods or scientific computing. Finally, we
emphasize the use of adaptivity as general concept and for boundary
element methods in particular.

In this work, we summarize recent analytical results on adaptivity in
the context of BEM and illustrate the use of HILBERT. Various
benchmarks are performed to empirically analyze the performance of
the proposed adaptive algorithms and to compare adaptive and uniform
mesh-refinements. In particular, we do not only focus on mathematical
convergence behavior but also on the usage of critical system
resources such as memory consumption and computational time. In any
case, the superiority of the proposed adaptive approach is
empirically supported.

http://dx.doi.org/10.1007/s11075-013-9771-2